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Groups Complexity Cryptology

Managing Editor: Shpilrain, Vladimir / Weil, Pascal

Editorial Board: Ciobanu, Laura / Conder, Marston / Dehornoy, Patrick / Eick, Bettina / Elder, Murray / Fine, Benjamin / Gilman, Robert / Grigoriev, Dima / Ko, Ki Hyoung / Kreuzer, Martin / Mikhalev, Alexander V. / Myasnikov, Alexei / Perret, Ludovic / Roman'kov, Vitalii / Rosenberger, Gerhard / Sapir, Mark / Thomas, Rick / Tsaban, Boaz / Capell, Enric Ventura

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Quantum algorithms for fixed points and invariant subgroups

Marianna Bonanome
  • Department of Applied Mathematics and Computer Science, New York City College of Technology CUNY, 300 Jay Street, Brooklyn, New York 11201, USA.
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/ Stephen Majewicz
Published Online: 2011-11-03 | DOI: https://doi.org/10.1515/gcc.2011.013


In this paper, we apply quantum algorithms to solve problems concerning fixed points and invariant subgroups of automorphisms. These efficient algorithms invoke a quantum algorithm which computes the intersection of multiple unsorted multisets whose elements originate from the same set. This intersection algorithm is an application of the Grover search procedure.

Keywords.: Quantum algorithm; Grover algorithm; quantum computation; fixed-point-free automorphism

About the article

Received: 2010-11-19

Published Online: 2011-11-03

Published in Print: 2011-12-01

Citation Information: Groups – Complexity – Cryptology, Volume 3, Issue 2, Pages 329–348, ISSN (Online) 1869-6104, ISSN (Print) 1867-1144, DOI: https://doi.org/10.1515/gcc.2011.013.

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